In a previous study we demonstrated that the initial ocular following responses (OFR) elicited by motion of a large pattern were severely attenuated if the pattern was shifted out of the plane of fixation by altering its binocular disparity. This was advanced as evidence that visual stabilization mechanisms utilize disparity to distinguish images moving in the plane of fixation from those moving in other depth planes, an everyday task confronting the observer who moves through a structured 3-D world. The stimulus profile in that study consisted of a step-ramp, the step being disconjugate (to introduce the disparity)and the ramp being conjugate (to elicit OFR).We now report that replacing the disconjugate step with a conjugate one yielded similar and only slightly weaker effects, indicating that much of the previously reported attenuation attributed to disparity might in fact have been due to the associated transient visual disturbance. If the steps were applied during a centering saccade and the ramp was initiated 50 ms after the eyes arrived at their new positions then the conjugate steps were now without effect on the initial OFR and the disconjugate steps had only a weak suppressive effect. Arguing that the use of a large homogeneous pattern was unnatural, we sought in a further experiment to simulate more faithfully the motion parallax experienced by the moving observer by dividing the (random-dot) pattern into horizontal bands that could be moved horizontally to induce OFR. The bands were organized into two groups, a test group that was imaged always in the plane of fixation, and a conditioning group that was imaged in the same or a different depth plane by adjusting its horizontal disparity during a centering saccade. Fifty milliseconds after the end of the saccade, the two groups of bands began to move in opposite directions, inducing OFR that increasingly favored the motion in the test bands as the conditioning bands were increasingly positioned outside the plane of fixation. If the displacements of the conditioning bands were conjugate they were without effect on OFR. Varying the time when the bands began to move indicated that the effect of disparity was essentially fully developed within 10 ms of the end of the saccade, too soon to be the result of a visually-induced (exogenous) shift of attention. We conclude from these experiments that initial OFR can use binocular disparity to respond selectively to images moving in the plane of fixation and to ignore images moving with competing motion in other depth planes. This means that the system tends to track whatever happens to be in the plane of fixation - the object(s) of regard - in a reflex-like fashion with ultra-short latencies without the necessity for any further, time consuming, target selection process.